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Diversity-optimized cooperation on complex networks

Han-Xin Yang1, Wen-Xu Wang2, Zhi-Xi Wu3, Ying-Cheng Lai2,4, and Bing-Hong Wang1,5

  • 1Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
  • 2Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA
  • 3Department of Physics, Umeå University, 90187 Umeå, Sweden
  • 4Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
  • 5The Research Center for Complex System Science, University of Shanghai for Science and Technology, Shanghai 200093, China

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Phys. Rev. E 79, 056107 – Published 19 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056107

Abstract

We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent α is an adjustable parameter that controls the level of diversity among individuals in the network. During the evolution, every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor, and updates its strategy depending on their payoff difference. It is found that there exists an optimal value of α, for which the level of cooperation reaches maximum. This phenomenon indicates that, although high-degree individuals play a prominent role in maintaining the cooperation, too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation. Other pertinent quantities such as the payoff, the cooperator density as a function of the degree, and the payoff distribution are also investigated computationally and theoretically. Our results suggest that in order to achieve strong cooperation on a complex network, individuals should learn more frequently from neighbors with higher degrees, but only to a certain extent.

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Phys. Rev. E 79, 056107– Published 19 May, 2009
  • Received 11 December 2008

© 2009 American Physical Society

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